9514 1404 393
Answer:
$4.92
Step-by-step explanation:
The cost is found by multiplying the number of feet by the cost per foot. The number of feet is the perimeter of the dining room, the sum of the lengths of all the sides.
There are two sides of the rectangular room that are 19 feet, and two sides that are 22 feet, so the total length of trim is ...
P = 2(L +W) = 2(22 ft + 19 ft) = 2(41 ft) = 82 ft
The cost is then ...
cost = ($0.06/ft)(82 ft) = $4.92
It will cost Luna $4.92 to buy enough trim.
In ΔQRS, m∠Q = 11° and m∠R = 40°. Which list has the sides of ΔQRS in order from shortest to longest?
PLEASE HELP!!
Answer:
RS, SQ, QR
Step-by-step explanation:
The three angles in a triangle add up to 180° Two angles are given, so we can find the third angle.
11 + 40 + S = 180
51 + S = 180
subtract 51
S = 129°
S is the biggest angle, so the biggest side will be opposite from S. QR is the biggest side.
AngleQ is 11°, the smallest angle. The smallest side will be opposite from the smallest angle. The smallest side is RS.
The 40° angle, AngleR is in the middle. The medium length side is opposite from the medium size angle. SQ is the medium length side.
From small to big:
RS, SQ, QR
Answer:
The 4th answer down
RS, SQ, RQ
Step-by-step explanation:
There is a relationship between the angle measurement and the length of the side opposite of the angle. The side opposite of the largest angle measurement has the longest side opposite to that angle, the same is true for the middle angle and the smallest angle.
During the year, Salaries Payable decreased by $12,000. Using the direct method of reporting cash flows from operating activities, if Salaries Expense amounted to $450,000 for the year, the cash paid to employees (including deductions from gross pay) is
If during the year, Salaries Payable decreased by $12,000. Using the direct method of reporting cash flows from operating activities, if Salaries Expense amounted to $450,000 for the year, the cash paid to employees is $462,000.
What is cash paid?Cash paid can be defined can be defined as the amount that is payable to an employee by an employer.
Using this formula to find the cash paid to employees
Cash paid to employees = Salaries payable decreased + Salaries Expense
Where:
Salaries payable decreased = $12,000
Salaries expense = $450,000
Let plug in the formula
Cash paid to employees = $450,000 + $12,000
Cash paid to employees = $462,000
Therefore the Cash paid to employees is the amount of $462,000.
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What are x and y if angle A is (2x), angle B is (y+x), and angle C is (y-x)?
Value of x is 30 and y is 30, if angle A is (2x), angle B is (y+x), and angle C is (y-x).
Define angle.The names of fundamental angles include acute, obtuse, right, straight, reflex, and full rotation. A geometrical shape called an angle is created by connecting two rays at their termini. In most cases, an angle is expressed in degrees. In geometry, there are several different kinds of angles. a geometric shape made up of two lines that meet at the same point or two planes that meet at the same line. the distance in degrees between such lines or planes.
Given
Angle A = 2x
Angle B = y + x
60 = y + x
y = 60 - x
Angle C = y - x
60 = y - x
60 + x = y
As we know, sum of triangle is 180
2x + 60 - x + 60 + x = 180
2x - x + x = 180 - 120
2x = 60
x - 30
For value of y, equating value of x in y = 60 - x
y = 60 - 30
y = 30
Value of x is 30 and y is 30, if angle A is (2x), angle B is (y+x), and angle C is (y-x).
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Work out angle bcc give a reason for each angle you work out
Answer:
70 degrees
Step-by-step explanation:
Triangle XBC is an isosceles triangle.
From the question given, you already know that angle XBC = 55 degrees. This means that angle XCB = 55 degrees. This is because the two sides XB and XC are of equal length, which means that the angles are also equal to each other.
Using this info, we can calculate angle BXC:
The sum of a triangle adds up to 180, so call the unknown angle x:
55 + 55 + x = 180
110 + x = 180
x = 180 - 110 = 70 degrees
A student paid 13% value added tax (VAT) after receiving 8% discount from the seller while purchasing a mobile set to participate in online class. If the student paid Rs. 10396 to purchase the mobile set, by how much the price paid by the student or the price marked by the seller is more? Find.
Answer: 113% = 9153
100% = ?
100/113 X 9153 = 915300/113 = Rs 8100 = sale price
90 % = 8100
100% = ?
100/90 X 8100 = Rs 9000 = marked price
108% = 8100
100% = ?
100/108 X 8100 = Rs7500 = cost
Difference = 9000 -7500 = Rs 1500
1500/7500 X 100 = 20%
ANSWER Marked price is 20% above cost price
Step-by-step explanation:
a planes average speed was 340 miles per hour how long did it take the plane to travel 1190 miles
Given average speed=340 miles per hour
speed= distance/time (formula)
speed= 340/60
speed=5.6 miles/min
now,we have to calculate time,
time=distance/speed
time=1190/5.6
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A four year lease agreement requires payments of 10000php at the begginning of every year if the interest is 6% compounded monythly what is cash value of the lease
Answer:
36647.36
Step-by-step explanation:
Lease payment =$1000
interest rate= 6%, compounded monthly
Time = 4 years
We have to calculate the present value
PV = 10000 + 10000/(1+ 0.06/12)^12 + 10000/(1+0.06/12)^24+ 10000(1+0.06/12)^36 = 36647.36
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Construct a geometric mean between a and c.
Geometric mean will be a line segment with length x such that x² = a × c.
What is Geometric Mean?Geometric mean of two line segments p and q is a line x such that it satisfies the formula x² = a × b or x/a = b/x.
To construct geometric mean, first simply draw a line segment and mark a point P anywhere on this line.
Mark the length of the line segment 'a' from the point P and mark the endpoint of 'a' as A. Now, in the same line, from the point P, mark the length of the given line 'c' and mark its endpoint as C.
Now, draw a perpendicular bisector of the resulting line PC. Then we get the midpoint of PC. Let this point be O.
Draw a semicircle with center O and the endpoints P and C.
Now draw a vertical perpendicular line from the point A until it cuts the semicircle. Let N be the point where this line touches the semicircle.
Now join P with N.
The line PN will be the geometric mean x such that a × c = x².
Hence the line segment PN is the geometric mean with length x.
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G(X)=-3x+2 find g(2)
Answer:
-4
Step-by-step explanation:
[tex]-3*2 + 2=-4[/tex]
Time to think about your New Year's Resolution for the new year. Nora decided she needed more
exercise. She decided that starting with the first full week in 2023, she will do a 45-minute workout
four times a week ( four days during every seven-day week.) This means she will exercise four of the
days during the week of Jan, 1 through Jan. 7 and will do the same during the week from Jan. 8
through Jan. 14, etc. If Nora sticks to her resolution, what is the first possible date on which she will
complete 25 hours of exercise for the year?
The first possible date on which she will complete 25 hours of exercise for the year is on March 1.
How to calculate date?In general, dates can refer to a specific day on the calendar, such as January 1 or December 31. Dates can also refer to a specific point in time, such as a specific hour, minute, or second. In some cases, dates can also refer to a specific period of time, such as a year, month, or week.
Since Nora plans to do a 45-minute workout four times a week,
she will exercise for a total of 4 * 45 minutes = 180 minutes per week.
This means that each week, she will exercise for a total of 180 / 60 = 3 hours.
To complete 25 hours of exercise for the year,
Nora will need to exercise for a total of 25 / 3 = 8.3 weeks.
The first possible date on which she will complete 25 hours of exercise is therefore 8.3 weeks after Jan 1,
Which is approximately 8.3 * 7 = 58 days after Jan 1.
Therefore, the first possible date on which Nora will complete 25 hours of exercise is 58 days after Jan 1, which is on March 1.
Overall, if Nora sticks to her New Year's resolution to exercise four times a week, the first possible date on which she will complete 25 hours of exercise for the year is on March 1.
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How to find the value of a + b + c.
I know the answer but I do not know how to arrive at the answer:
[tex]answer = 9[/tex]
The attached picture is of a similar problem. But different radii.
Notice how you can form 2 equilateral triangles, and that there are 4 semi circles (at AC, AD, BC, BD).
This is because points C and D lie on the circumference of the circles. So distance from centres( A and b) to C and D are the radius
To get the area of your shaded section, you would just need to add up the areas of the 4 semi circles and 2 equi. triangles.
To get the area of a semi circle, work out the area of one of the sectors, i.e sector ABC, then subtract area of an equilateral triangle.
(Note, due to symmetry all semi circles have same area)
________________________________________________________
For example, for the picture below:
Area of equi triangle = absinC = 1*1*sin60 = √(3) --> (C is angle)
Area of sector = (angle/360) * πr² = (60/360) * π * (1)² = π/6
So area of 1 semi circle = Area of Sector - Area of equi triangle
= π/6 - √(3)
Now you would just add the areas of 4 semi circles, and 2 equi triangles, and compare coefficients to get a, b, c.
______________________________________
Now you would do the same for your question, except radius is now 6cm instead of 1cm.
As part of a probability experiment for math class, Reid flipped a coin a hundred times. He
predicted it would land on heads 50 times, but it actually landed on heads 40 times. What is
the percent error for Reid's prediction?
►
If necessary, round your answer to the nearest tenth of a percent.
Answer:
25%
Step-by-step explanation:
we know that you have to do amount of error/ correct amount
so the amount of error is 10 and the correct amount is 40, so its 10/40.
10 divided by 40 is 0.25. They want the answer as a percent, so in order to turn 0.25 to a percent, you have to move the decimal 2 times over. It then turns into 25%
Nikola likes to play horseshoes, where players try to score a ringer by throwing a horseshoe so it lands around a post. A player gets 2 attempts each round. Let R represent the number of ringers that Nikola scores in a round. Here's the probability distribution of R along with summary statistics. R=# of ringers 0 1 2 P(R) 0.75 0.20 0.05 Mean: HR=0.3 Standard deviation: OR 0.56 Nikola gets 3 points for each ringer that he scores. Let X represent the number of points that Nikola gets from ringers in a round. What are the mean and standard deviation of X?
The mean and standard deviation of X are 0.9 and 1.68 points.
Since Nikola gets 3 points for each ringer which he scores, then total points he gets from ringers could be determined by multiplying the number of ringers by 3.
So, X = R * 3 = 3R
Where:
R = numbers of ringers
X = total points Nikola gets from ringers
Given:
Mean : μR = 0.3
Standard deviation : σR = 0.56
Thus, multiplying by 3 will effects the mean as follows:
μX = 3 (μR)
= 3 (0.3)
= 0.9
And, multiplying by 3 also will effects the standard deviation as follows:
σX = 3 (σR)
≈ 3 (0.56)
≈ 1.68
Hence, the mean of X is 0.9 and and the standard deviation of X is 1.68.
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1. Suppose there
are 4 people and 9 different assignments. Each person should receive one
assignment. Assignments for different people should be different. How many ways
are there to do it?
The ways to assign for different people is 126 ways
How to determine the ways of selection?From the question, we have
Total number of questions, n = 9
Numbers to people, r = 4
The number of ways of selection could be drawn is calculated using the following combination formula
Total = ⁿCᵣ
Where
n = 9 and r = 4
Substitute the known values in the above equation
Total = 9C4
Apply the combination formula
ⁿCᵣ = n!/(n - r)!r!
So, we have
Total = 9!/5!4!
Evaluate
Total = 126
Hence, the number of ways is 126
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4 adults took their 5 children to a movie. The price for the 9 people was $160. The 5 children recieved a 20% discount on their tickets. The cost for a child ticket is how much less than the cost of an adult ticket?
Answer:
The answer is $14.224.
Step-by-step explanation:
65. Which of the following could represent the side
lengths of a triangle? Check all that apply.
A. 6, 10, 14
B. 12, 15, 29
C. 8, 8, 11
D. 19, 24, 40
E. 9, 17, 26
Answer: The following that could represent the side lengths of a triangle are A, C, D.
Step-by-step explanation:
The sum of the first two numbers of the triangle must be greater than the third.
A. 6+10= 16>14 -----------a triangle
B. 12+15= 27<29 -----------not a triangle
C. 8+8= 16>11 -----------a triangle
D. 19+24= 43>40 ------------a triangle
E. 9+17= 26=26 -------------not a triangle
Hope this helps! :)
What is the slope?????????
Answer:
AB - [tex]\frac{2}{1}[/tex]
BC - [tex]\frac{4}{2}[/tex]
AC - [tex]\frac{6}{3}[/tex]
Slope = 2
Step-by-step explanation:
For AB the rise (counting upwards) is 2 and the run (counting to the right) is 1. If you simplify it, it would be 2. The reason why it's not a negative is that the slope is going upwards not downwards.
Help!!!!!! See image.
The shape of the graph of a function is the shape assumed by the graph of the function after the dataset generated by using the function is plotted on the coordinate plane. The shape in the graph of the question is a triangular shape.
What is a function?A function is a direction used to map the values of an input variable of the function to the output variables.
The points in the attaches graph which are connected by lines are;
(0, 1.5), and (4.5, 0)
The joining of the above points in the attached graph, and the origin forms a triangular shape.
Details about the shape of the graph of a function
The graph of a function such as f(x) = -x² + 2·x + 3, is obtained by finding the values of the output values of the function, f(x) for each input value of the function, x as follows;
x [tex]{}[/tex] f(x)
0 [tex]{}[/tex] 3
1 [tex]{}[/tex] 4
2 [tex]{}[/tex] 3
3 [tex]{}[/tex] 0
4 [tex]{}[/tex] -5
5 [tex]{}[/tex] -12
6 [tex]{}[/tex] -21
7 [tex]{}[/tex] -32
8 [tex]{}[/tex] -45
Please find attached the graph of the sample function created with MS Excel
The graph of the function f(x) = -x² + 2·x + 3 has the shape of a parabola, which is the shape of a quadratic function.
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The numerator of a fraction is 5 less than its denominator. If 1 is added to the numerator and to the denominator, the new fraction is [tex]\frac{2}{3\\}[/tex] Find the fraction.
The fraction in the question is 9 / 14
FractionsFractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.
To solve this problem, we have to write an algebraic equation and solve for the unknown.
Assuming x represents the unknown value
Original fraction = x - 5 / x
When 1 is added to both numerator and denominator;
x - 5 + 1 / x + 1 = 2/3
x - 4 / x + 1 = 2/3
Cross multiplying both sides
2(x + 1) = 3(x - 4)
2x + 2 = 3x - 12
Collect like terms and solve for x
2 + 12 = 3x - 2x
x = 14
The fraction is 14 - 5 / 14 = 9 /14
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calculate the volume, in milliliters, of hbrhbr solution required to neutralize 28.0 mlml of a 0.210 mm liohlioh solution . express your answer using three significant figures.
The volume, in milliliters, of hbrhbr solution required to neutralize 28.0 mlml of a 0.210 mm liohlioh solution is 1.176 ml.
Volume is a degree of the quantity of area that be counted occupies. Matter is described as a bodily substance that occupies area and has a mass. In bodily sciences like chemistry, the usual unit of extent is cubic metres (m3). From this, different gadgets are derived inclusive of litre (L) and millilitre (mL).
A correct region to begin is the balanced chemical equation for this neutralization: 2 H Br + Ba (OH)2 → Ba Br2 + 2 H2O The crucial aspect right here is that it takes moles of H Br to neutralize one mole of Ba(OH)2 . The variety of moles of Ba(OH)2 is 0.28x 0.210 =0.0588 moles. Thus 2 x .0.0588 = 1.176 moles of H Br are wished. The extent, V, of H Br answer wished may be computed from V) = 1.176 L.
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What is the answer to this question?
A. Domain: All Real Numbers; Range: All Real Numbers
B. Domain: −10 ≤x≤10 Range: −4≤y≤8
 patrick takes a textbook to a pawnshop to borrow some money and is given $30.00. Patrick must pay back the $30.00 in addition to a $12.50 fee in 6 months.
What simple interest rate is he being charged?
Answer:
here,
simple interest (S)=12.50$
Principal(p)=30.00$
time(t)=0.5 year
Now,
S=PTR/100
or,12.50=30×0.5×R/100
or,1250=15R
or,1250/15=R
:.R=83.33% per annum
Consider this diagram.
(6x+30)
(8x+10)
Given: m/CEA (8+10): m/AED
Prove: - 10
Statement
Part A
Mr. Avila asked his students to write either a two-column proof or a paragraph proof for the question shown.
Student A and Student B each made a mistake in their proof. Identify each student's mistake and the step in which they
made it.
Type your response in the box.
mZCRA
mZAED
838°
ZCEA and ZAED are a near
pair.
m/CEA + m/AED
8z + 10 + 6x + 30
14x + 40 180
14 140
-10
Student A's Proof
and
=
180°
L 180
(6m+30)
Reason
given
definition of linear pair
Linear pairs are
supplementary.
substitution
Like terms can be combined.
addition property of equality
division property of equality
Student B's Proof
We are given that mZCEA (8 + 10) and
m/AED = (6x +30) By the definition of vertical
angles, we know that ZCEA and ZAEDare vertical
angles. Vertical angles have equal measures, so
m/CEA m/AED substituting
m/CEA -
3x + 10and m/AED - 6x + 30 into
m/CEA
ZAED, we get
8+10= 6z+ 30. Using the subtraction property
of equality on the variable terms, this becomes
2z+10 30. Using the subtraction property of
equality on the constants, we get 2z - 20 By the
division property of equality, we prove that m 10
-
-
The angles m∠CEA and m∠AED are supplementary .hence the value of x will be 10 has been proved.
What is an angle?An angle is a geometry in plane geometry that is created by 2 rays or lines that have an identical terminus.
The identical endpoint of the two rays known as the vertex—is referenced as an angle's sides.
We are Given that m∠CEA and m∠AED are only two angles on a straight line thus they will be supplementary.
Therefore, we have
m∠CEA + m∠AED = 180°
8x + 10 + 6x + 30 = 180
14x + 40 = 180
14x = 140
x = 10
Hence "The value of x will be 10 that proved the angles m∠CEA and m∠AEDare complementary".
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classify the following random variable according to whether it is discrete or continuous. the number of goals scored in a hockey game
The number of goals scored in a hockey game is a discrete random variable.
A discrete random variable has a countable number of different possible values, such as 0,1,2,3,4, etc. Usually, but not always, discrete random variables are counted. If a random variable has a limited range of possible values, it is discrete.
The number of children in a household, the Friday night movie attendance, the number of patients at a doctor's office, and the number of faulty light bulbs in a box of ten are a few examples of discrete random variables. A discrete random variable's probability distribution is a table of the probabilities connected to each of its potential values.
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If you tossed two coins simultaneously 400 times, would you expect the deviation to be greater or less than it was in tossing them 40 times? Explain.
Yes, the deviation is greater than it was in tossing them 40 times.
What is Standard Deviation?A standard deviation (or σ) is a measure of how widely distributed the data is in reference to the mean. A low standard deviation suggests that data is grouped around the mean, whereas a large standard deviation shows that data is more spread out.
Given:
n= 400 trials
Tossing 2 coins 400 times gives 800 trials
so, [tex]\sigma_1[/tex]² = np(1- p)
= 800 x 1/2 x 1/2
[tex]\sigma_1[/tex] = √200
[tex]\sigma_1[/tex] = 10√2
Now, n=40
and, [tex]\sigma_2[/tex]² = np(1- p)
= 80 x 1/2 x 1/2
[tex]\sigma_2[/tex] = √20
[tex]\sigma_2[/tex] = 2√5
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A triangle is shown in the image.
What is the area of the triangle represented?
A: 204 in2
B: 216 in2
C: 408 in2
D: 432 in2
Answer:
B. 216 in²
Step-by-step explanation:
You want to know the area of a triangle with a base of 36 inches and a height of 12 inches.
Area formulaThe area of a triangle is given by ...
A = 1/2bh
where b is the base of the triangle (one side), and h is the height to the opposite vertex, measured perpendicular to the base.
ApplicationThe figure shows a base of 36 inches and a height of 12 inches. Using these values in the formula, we have ...
A = 1/2(36 in)(12 in) = 216 in²
The area of the triangle is 216 in².
Answer: 216
Step-by-step explanation: I got it right sorry for the late comment
i will make you brainiest ok
Answer:
11/20
Step-by-step explanation:
4/5 - 1/4
find greatets common denominator aka 20 cuz 5 and 4 can go into 20
multiply that many tiems it goes into 20 for the numerator
you now have 16/20 - 5/20
the answer is 11/20
Solve for x in the equation x2-14x+31-63-
Ox=-16 or x = 2
O x=-7±3-√√7
Ox=-2 or x = 16
Ox=7±3√√√7
Answer:Value of x are 16 and -2
Step-by-step explanation:
Solve for x in the equation:
Subtract 63 from both sides we have;
To factor this equation as:
⇒
Take (x-16) common we have;
⇒
By zero product property we have;
x-16 = 0 or x+2 = 0
⇒x = 16 or x = -2
Therefore, the value of x are: 16 and -2
The value of x in the equation are x = -2 or x = 16.
What are Quadratic Equations?Quadratic equations are polynomial equations of second degree.
The general form of a quadratic equation is ax² + b x + c = 0.
Given is a quadratic equation,
x² - 14x + 31 = 63
We have to find the value of x.
x² - 14x + 31 - 63 = 0
x² - 14x - 32 = 0
Using the quadratic formula,
x = [14 ± [tex]\sqrt{(-14)^2-(4*1*-32)}[/tex]] / 2
= (14 ± √324) / 2
= (14 ± 18) / 2
x = 14 + 18 / 2 or x = 14 - 18 / 2
x = 16 or x = -2
Hence the value of x are x = 16 or x = -2.
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How much would you need to deposit in an account now in order to have $6,000.00 in the account in 389
days?
Assume the account earns 2-% simple interest.
You would need to deposit_____ in your account now.
Answer:
$5,851.88
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{7 cm}\underline{Simple Interest Formula}\\\\$ A = P(1 + rt)$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]
Given values:
A = $6000r = 2³/₈% = 0.02375t = 389 days = ³⁸⁹/₃₆₅ yearsSubstitute the given values into the formula and solve for P:
[tex]\implies 6000=P\left(1+0.02375 \times \dfrac{389}{365}\right)[/tex]
[tex]\implies P=\dfrac{6000}{1+0.02375 \times \dfrac{389}{365}}[/tex]
[tex]\implies P=\dfrac{6000}{1+0.0253116438...}[/tex]
[tex]\implies P=\dfrac{6000}{1.0253116438...}[/tex]
[tex]\implies P=5851.87931....[/tex]
Therefore, you would need to deposit $5,851.88 in your account now.
solve each of the following quadratic inequalities using any Convenient
method :
A)
[tex]x(10x + 19) \leqslant 15[/tex]
[tex](x + 2)^{2} > (3x + 1)^{2} [/tex]
Answer:
-2.5 ≤ x ≤ 0.6-0.75 < x < 0.5Step-by-step explanation:
You want the solutions to the following inequalities by any convenient method:
x(10x +19) ≤ 15(x +2)² > (3x +1)²ComparisonWe choose to rewrite these inequalities to be comparisons to zero. This is because our graphing calculator easily identifies the x-intercepts of a graph. We can look a the graph to tell where the function is above or below the x-axis.
f(x) = x(10x +19) -15; f(x) ≤ 0g(x) = (x +2)² -(3x +1)²; g(x) > 0GraphThe attached graph shows the solutions to be ...
f(x) ≤ 0 for -2.5 ≤ x ≤ 0.6g(x) > 0 for -0.75 < x < 0.5The values obtained for the first equation will be x ≤ 3/5 and x ≤ -5/2 and the values obtained for the second equation will be x < 1/2 and x < -3/4.
What is inequality?Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare the two values. Less than (or less than and equal to), larger than (or greater or equal to), or not similar to signs are used in place of the equal sign in between.
As per the given inequalities in the question,
1.
x(10x + 19) ≤ 15
Firstly, simplify it to the simpler form,
10x² + 19x - 15 ≤ 0
Solve the quadratic equation,
D = b² - 4ac
= 19² - 4(10)(-15).
D = 961
Now, use the formula,
(-b±√D)/2a
√D = √961 = 31
(-19 ± 31)/2(10)
So, the roots are:
1.
(-19 + 31)/20 = 12/20 = 3/5
Or, x ≤ 3/5
2.
(-19 - 31)/20 = -50/20 = -5/2
Or, x ≤ -5/2
2.
(x + 2)² > (3x + 1)²
Simplify the equation first.
x² + 4x + 4 > 9x² + 6x + 1
x² - 9x² + 4x - 6x + 4 - 1 > 0
-8x² - 2x + 3 >
8x² + 2x - 3 < 0
Now, find the roots for the equation,
D = b² - 4ac
D = 4 + 96
D = 100
Now, use the formula,
(-b ± √D)/2a
(-2 ± 10)/16
So, the roots are:
1. (-2 + 10)/16 = 1/2
Or, x < 1/2
2. (-2 - 10)/16 = -12/16 = -3/4
Or, x < -3/4
To know more about Inequality:
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